cianfa72's latest activity

Indeed, given the Langevin congruence (i.e. the orbits of the timelike vector field ##\xi^a##) your projection operator on the quotient...

The point I was trying to make is technical. The set of smooth tensor fields of a given type on the smooth manifold M isn't a vector...

Yes. The point is that we have a tensor field (the metric tensor field ##g_{ab}##) and a timelike congruence ##\xi^a##. The latter...

Yes, agreed. Indeed the projection applies to the set of tensor fields defined on a tensor product bundle fiberwise (in this case twice...

I had to look this up, possibly there is some confusion over wording. What I wrote was in the thread on Born rigidity, and what the...

I think this depends on the definitions used. For example in Lecture 18: Canonical Formulation of GR I, the metric tensor field...

The hypersurfaces are 3-dimensional; therefore, any projection onto them must also be 3-dimensional.

Ah ok, transverse to both of them. Yes, that was my point (where ##i,j## run for 1,2,3). BTW, I believed that the projection of ##g##...

Yes. They are the composite conditions for Lorenz + TT gauge. Namely, in Lorenz gauge $$\partial_{\mu}h^{\mu}{}_{\nu} - \frac {1} {2}...

Ok, so that means that even though ##h_{\mu\nu} \left( \frac {\partial} {\partial_t} \right)^{\nu}= 0## , the metric ##g## restricted to...

As I recall transverse refers to ##\partial^\mu h_{\mu\nu} =0## which is the case. EM waves are transverse in that E and H are...

I believe ##h_{\mu\nu}## isn't the transverse part of the metric tensor field ##g## w.r.t. the timelike congruence given by integral...

Coming back to TT gauge coordinates, the components of the metric tensor field ##g## in that chart are $$g_{\mu \nu} = \eta_{\mu \nu} +...

Let's say we transform from SC exterior chart (that's defined for ##r > 2m, - \infty < t < \infty##) coordinates to Kruskal-Szekeres...

Note that LIGO doesn't measure arm length. It's an interferometer, so what it measures is differences in flight time between the two...